$10 is a lot of money to waste on parking. Let's face it, there is no need to pay if you are willing to walk a few blocks and don't mind a shuttle bus.
Simply use the free street parking that is available around town deep in the neighborhoods and either walk or ride your bicycle to the Hershey Museum. Watch the street signs because some streets have only 2 hour parking. Behind and to the right of the Hershey Museum you can walk across an enclosed overpass walkway. Once across you can wait for the free shuttle bus that operates when Hershey Park and Hershey Museum is open. It will take you to Hershey Park. The shuttle hours vary so make sure you find out what they are so you can plan your return. You can walk to the park too. Either use the overpass walkway or the Park Avenue Bridge and follow the asphalt path from there. Once you arrive at Chocolate World you can walk to the Stadium or the Giant Center quite easily. See map for details.
The Shuttle bus is free for visitors of Chocolate World and the Hershey Museum. It costs nothing to be a visitor at the Museum gift shop and Chocolate World. In fact, the Chocolate World ride is free and they give you free candy samples at the end. Might as well enjoy the air conditioning while you are there. After you "visit" you can continue on to the Giant Center or Stadium and do what you need to do.
Here is a link to this Google Map.
While riding the shuttle bus this may not be a good time to give a lecture on the evils of indulging on sugar, lack of exercise and childhood morbid obesity. Trust me, this won't be a receptive crowd.